Synchronization

1. Synchronization Shanghai Jiao Tong University

2. Synchronization Synchronization is one of the most critical functions of a communication system with coherent receiver. To some extent, it is the basis of a synchronous communication system. • Carrier synchronization • Symbol/Bit synchronization • Frame synchronization

3. Synchronization • Carrier synchronization (载波同步） Receiver needs estimate and compensate for frequency and phase differences between a received signal’s carrier wave and the receiver’s local oscillator for the purpose of coherent demodulation, no matter it is analog or digital communication systems

4. Synchronization • Frame synchronization （帧同步） In frame-based digital systems, receiver also needs to estimate the starting/stopping time of a data frame. The process of extracting such a clock signal is called frame synchronization. • Symbol/bit synchronization (符号/位同步） In digital systems, the output of the receiving filter (i.e. matched filter) must be sampled at the symbol rate and at the precise sampling time instants. Hence, we require a clock signal. The process of extracting such a clock signal at the receiver is called symbol/bit synchronization.

5. Phase-locked Loop PLL （锁相环）is often used in carrier syn. and symbol syn. It is a closed-loop control system consisting of • Phase detector (PD): generate the phase difference of vi(t) and vo(t). • Voltage-controlled oscillator (VCO): adjust the oscillator frequency based on this phase difference to eliminate the phase difference. At steady state, the output frequency will be exactly the same with the input frequency. • Loop filter (LF)

6. Phase-locked Loop A PD contains a multiplier and a lowpass filter. The output of PD is: Loop filter is also a LPF. 。 The output of the LF is (where F(p) is the transfer function)

7. Phase-locked Loop The output of VCO can be a sinusoid or a periodic impulse train. The differentiation of the output frequency are largely proportional to the input voltage. If F(p)=1，Then This kind of loop is called the first-order loop

8. DPLL Input Digital PD Digital LP Digital VCO output 图9-6 DPLL的组成 Digital PLL

9. Phase-locked Loop In a coherence system, a PLL is used for: • PLL can track the input frequency and generate the output signal with small phase difference. • PLL has the character of narrowband filtering which can eliminate the noise introduced by modulation and reduce the additive noise. • Memory PLL can sustain the coherence state for enough time. CMOS-based integrated PLL has several advantages such as ease of modification, reliable and low power consumption, therefore are widely used in coherence system.

10. Carrier Synchronization To extract the carrier： 1. Pilot-tone insertion method Sending a carrier component at specific spectral-line along with the signal component. Since the inserted carrier component has high frequency stability, it is called pilot (导频). 2. Direct extraction method Directly extract the synchronization information from the received signal component.

11. Modulator Add s(t) x(t) Bandpass filter -asin(ct) /2phase shift cos(ct) Pilot-tone insertion method 1. Pilot-tone insertion method －insert pilot to the modulated signal Thinking： Why 900 shift？ The pilot signal is generated by shift the carrier by 900 and decrease by several dB, then add to the modulated signal. Assume the modulated signal has 0 DC component, then the pilot is

12. Pilot-tone insertion method S(f) X(f) 0 0 fx f fc fc-fx fc+fx The receiver uses a narrowband filter with central frequency fc to extract the pilot and then the carrier can be generated by simply shifting 900.

13. Pilot-tone insertion method DSB, SSB and PSK are all capable of pilot-tone insertion method. VSB can also apply pilot-tone insertion method but with certain modification.

14. Narrowband Filter The drawback of narrowband filter: • The pass band is not narrow enough • fc is fixed, cannot tolerate any frequency drift with respect to the central frequency • Can be replaced by PLL Pilot-tone insertion method is suitable for DSB, SSB, VS and 2PSK

15. Direct extraction method 2. Direct extraction method 1).If the spectrum of the received signal already contains carrier component, then the carrier component can be extracted simply by a narrowband filter or a PLL. 2).If the modulated signal supresses the carrier component, then the carrier component may be extracted by performing nonlinear transformation or using a PLL with specific design.

16. Nonlinear-transformation-based method 1. Square transformation

17. Nonlinear-transformation-based method

18. Nonlinear-transformation-based method • Square PLL

19. In-phase orthogonal loop—Costas Loop 2. In-phase orthogonal loop—Costas Loop Contains in-phase branchand orthogonal branch. All parts except LF and VCO are similar with a “phase detector”.

20. In-phase orthogonal loop—Costas Loop

21. Performance 3. Performance of carrier synchronization technique 1) Phase error: steady-state phase error, random phase error 2) Synchronization build time and hold time

22. Symbol Synchronization • In a digital communication system, the output of the receiving filter must be sampled periodically at the symbol rate and at the precise sampling time instance. • To perform this periodic sampling, we need a clock signal at the receiver • The process of extracting such a clock signal is called symbol synchronization or timing recovery • One method is for the transmitter to simultaneously transmit the clock frequency along with the information signal. The receive can simply employ a narrowband filter or PLL to extract it. This method requires extra power and bandwidth and hence, but frequently used in telephone transmission systems. • Another method is to extract the clock signal from the received data signal by using some kind of non-linear transformation.

23. Early-Late Gate Synchronization • Basic Idea: exploit the symmetry properties of the output signal of matched filter or correlator • Due to the symmetry, the values of the correlation function at the early samples and the late samples are equal. • Thus, the proper sampling time is the midpoint between and

25. Nonlinear-transformation-based method 1. Nonlinear-transformation-based method Some transformations can add synchronous signal with f=1/T to the original signal. For example, we can transform the signal to return-to-zero waveform. After narrowband filtering and phase shifting, we can generate the clock signal used for synchronization.

26. Digital PLL (DPLL) 2. DPLL

27. Digital PLL (DPLL)

28. Performance 3. Performance of symbol synchronization system —DPLL 1). Phase error 2). Synchronization build time 3). Synchronization hold time 4). Synchronous bandwidth

29. Frame Synchronization • Recall that carrier and symbol synchronization needs to estimate the phase of synchronous signal which can be realized by using a PLL. • Frame synchronization is to insert frame alignment signal (distinctive bit sequence) and then detect the alignment symbol. • Besides adding frame alignment bits, some code such as self-synchronizing code can be synchronized without adding extra bits. • Here, we only focus on the first method ——inserting frame alignment signal.

30. Frame Synchronization • Start-stop method • Bunched frame alignment signal • Distributed frame alignment signal

31. Start-stop Method 1. Start-stop method It is widely used in teleprinter. Each symbol contains 5-8 data bits, a start bit and a stop bit.

32. Start-stop Method Drawbacks: 1). Low transmission efficiency 2). Low timing accuracy

33. Bunched frame alignment signal 2. Bunched frame alignment signal This method inserts synchronous code at a particular place in each frame. The code should have a sharp self-correlation function. The detector should be simple to implement. Frame synchronization code: • Barker code • optimal synchronous code • pseudo-random code.

34. Barker Code

35. Barker Code n barker code 2 + + 3 + + - 4 + + + - ，+ + - + 5 + + + - + 7 + + + - - + - 11 + + + - - - + - - + - 13 + + + + - - + + - + - +

36. Barker Code

37. Barker Code (2)Barker code generator —shift register Example：when n=7, a 7 bits shift register. The initial state is a barker code.

38. Barker Code (3) Barker code detector

39. Barker Code

40. Distributed frame alignment signal 3. Distributed frame alignment signal The synchronous code is distributed in the data signal. That means between each n bits, a synchronous bit is inserted. Design criteria of synchronous code: 1. Easy to detect. For example: “11111111”or ”10101010” 2. Easy to separate synchronous code from data code. For example: In some digital telephone system，all ”0” stands for ring, so synchronous code can only use “10101010”.

41. Performance Performance of frame synchronization system —Bunched frame alignment signal • Probability of missing synchronization PL Affected by noise, the detector may not be able to detect the synchronous code. The probability of this situation is called probability of missing synchronization PL. Assume the length of synchronous code is n，bit error rate is Pe. The detector will not be able to detect if more than m bit errors happen, then:

42. Performance 2. Probability of false synchronization PF Since data code can be arbitrary, it may be the same with synchronous code. The probability of this situation is called probability of false synchronization PF. PF equals to the probability of appearance of synchronous code in the data code. a. In a binary code, assume 0 and 1 appears with the same probability. There are 2n combinations of a n bit code. b. Assume when there are more than m bit errors, the data code will also be detected as synchronous code.

43. Performance

44. Performance

45. Suggested Reading • 《通信原理》，韩声栋、蒋铃鸽、刘伟 编著， 机械工业出版社, 2008.6, 第九章 • Chapter 8.6 of Fundamentals of Communications Systems, Pearson Prentice Hall 2005, by Proakis & Salehi